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Mass Spectra of $qq\bar{q}\bar{q}$, $ss\bar{s}\bar{s}$ and $qq\bar{s}\bar{s}$ Tetraquarks using Regge Phenomenology

Vandan Patel, Juhi Oudichhya, Ajay Kumar Rai

TL;DR

This study uses Regge phenomenology with a linear trajectory ansatz $J = \alpha(0) + \alpha' M^2$ to predict the mass spectra of all-light ($qq\bar{q}\bar{q}$), all-strange ($ss\bar{s}\bar{s}$), and light–strange ($qq\bar{s}\bar{s}$) tetraquarks. Ground-state masses are obtained from flavor-dependent Regge relations and then extended to excited states in both $(J,M^2)$ and $(n,M^2)$ planes by extracting slopes and intercepts, enabling mass predictions for higher orbital and radial excitations. The authors compare predictions to PDG resonances using a z-score based on a uniform theoretical mass interval, identifying strong or plausible matches for several states (e.g., X(1650), a2(1950), a4(2255), X(2075), a2(2175), X(2540), X(3250), X(3350), X(2680)). The results provide a cohesive, parameter-efficient framework for interpreting light and light-strange tetraquarks and yield concrete targets for future experimental validation, contributing to the non-perturbative QCD understanding of multiquark dynamics.

Abstract

In this paper, we explore the mass spectra of $qq\bar{q}\bar{q}$, $ss\bar{s}\bar{s}$ and $qq\bar{s}\bar{s}$ tetraquarks by employing Regge phenomenology. We calculate the range for ground state masses of $qq\bar{s}\bar{s}$ tetraquarks, and estimate the Regge parameters for their trajectories in $(J,M^2)$ plane. Using these Regge parameters we have calculated range for the excited state masses of $qq\bar{q}\bar{q}$, $ss\bar{s}\bar{s}$ and $qq\bar{s}\bar{s}$ tetraquarks in $(J,M^2)$ plane. Also, we have investigated the mass spectra of $qq\bar{q}\bar{q}$, $ss\bar{s}\bar{s}$ and $qq\bar{s}\bar{s}$ tetraquarks for their excited radial states in $(n,M^2)$ plane. We predict the potential quantum numbers of some newly observed experimental states, which necessitate additional validation, and assess the higher orbital and radial excited states that may be identified in the near future. The obtained mass relations and mass values of tetraquarks can be useful in future experimental searches and the spin-parity assignment of these states. Our findings provide valuable insights into the structure and properties of tetraquarks, contributing to the broader understanding of Quantum Chromodynamics (QCD).

Mass Spectra of $qq\bar{q}\bar{q}$, $ss\bar{s}\bar{s}$ and $qq\bar{s}\bar{s}$ Tetraquarks using Regge Phenomenology

TL;DR

This study uses Regge phenomenology with a linear trajectory ansatz to predict the mass spectra of all-light (), all-strange (), and light–strange () tetraquarks. Ground-state masses are obtained from flavor-dependent Regge relations and then extended to excited states in both and planes by extracting slopes and intercepts, enabling mass predictions for higher orbital and radial excitations. The authors compare predictions to PDG resonances using a z-score based on a uniform theoretical mass interval, identifying strong or plausible matches for several states (e.g., X(1650), a2(1950), a4(2255), X(2075), a2(2175), X(2540), X(3250), X(3350), X(2680)). The results provide a cohesive, parameter-efficient framework for interpreting light and light-strange tetraquarks and yield concrete targets for future experimental validation, contributing to the non-perturbative QCD understanding of multiquark dynamics.

Abstract

In this paper, we explore the mass spectra of , and tetraquarks by employing Regge phenomenology. We calculate the range for ground state masses of tetraquarks, and estimate the Regge parameters for their trajectories in plane. Using these Regge parameters we have calculated range for the excited state masses of , and tetraquarks in plane. Also, we have investigated the mass spectra of , and tetraquarks for their excited radial states in plane. We predict the potential quantum numbers of some newly observed experimental states, which necessitate additional validation, and assess the higher orbital and radial excited states that may be identified in the near future. The obtained mass relations and mass values of tetraquarks can be useful in future experimental searches and the spin-parity assignment of these states. Our findings provide valuable insights into the structure and properties of tetraquarks, contributing to the broader understanding of Quantum Chromodynamics (QCD).

Paper Structure

This paper contains 16 sections, 48 equations, 9 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Relationship between slope ratios and masses
  4. Linear mass inequalities and quadratic mass inequalities
  5. Mass Spectra of Tetraquark
  6. The four-quark state in diquark-antidiquark picture
  7. Mass Spectra of $qq\bar{q}\bar{q}$, $ss\bar{s}\bar{s}$ and $qq\bar{s}\bar{s}$ tetraquarks in the ($J,M^{2}$) plane
  8. Statistical comparison of predicted intervals and experimental masses
  9. Mass Spectra of $qq\bar{q}\bar{q}$, $ss\bar{s}\bar{s}$ and $qq\bar{s}\bar{s}$ tetraquarks in the $(n,M^2)$ plane
  10. Results and Discussion
  11. All light ($qq\bar{q}\bar{q}$) tetraquarks in $(J,M^2)$ plane
  12. Light-strange ($qq\bar{s}\bar{s}$) tetraquarks in $(J,M^2)$ plane
  13. Light ($qq\bar{q}\bar{q}$) tetraquarks in $(n,M^2)$ plane
  14. Light-strange ($qq\bar{s}\bar{s}$) tetraquarks in $(n,M^2)$ plane
  15. Conclusion
  16. ...and 1 more sections